The invention relates generally to a method and device for measuring the concentration of target chemical analytes present in a biological system. More particularly, the invention relates to a method and monitoring systems for predicting a concentration of an analyte using a series of measurements obtained from a monitoring system and a Mixtures of Experts (MOE) algorithm.
The Mixtures of Experts model is a statistical method for classification and regression (Waterhouse, S., xe2x80x9cClassification and Regression Using Mixtures of Experts, October 1997, Ph.D. Thesis, Cambridge University). Waterhouse discusses Mixtures of Experts models from a theoretical perspective and compares them with other models, such as, trees, switching regression models, modular networks. The first extension described in Waterhouse""s thesis is a constructive algorithm for learning model architecture and parameters, which is inspired by recursive partitioning. The second extension described in Waterhouse""s thesis uses Bayesian methods for learning the parameters of the model. These extensions are compared empirically with the standard Mixtures of Experts model and with other statistical models on small to medium sized data sets. Waterhouse also describes the application of the Mixtures of Experts framework to acoustic modeling within a large vocabulary speech recognition system.
The Mixtures of Experts model has been employed in protein secondary structure prediction (Barlow, T. W., Journal Of Molecular Graphics, 13(3), p. 175-183, 1995). In this method input data were clustered and used to train a series different networks. Application of a Hierarchical Mixtures of Experts to the prediction of protein secondary structure was shown to provide no advantages over a single network.
Mixtures of Experts algorithms have also been applied to the analysis of a variety of different kinds of data sets including the following: human motor systems (Ghahramani, Z. and Wolpert, D. M., Nature, 386(6623):392-395, 1997); and economic analysis (Hamilton, J. D. and Susmel, R., Journal of Economnetrics, 64(1-2):307-333, 1994).
The present invention provides a method and device (for example, a monitoring or sampling system) for continually or continuously measuring the concentration of an analyte present in a biological system. The method entails continually or continuously detecting a raw signal from the biological system, wherein the raw signal is specifically related to the analyte. A calibration step is performed to correlate the raw signal with a measurement value indicative of the concentration of analyte present in the biological system. These steps of detection and calibration are used to obtain a series of measurement values at selected time intervals. Once the series of measurement values is obtained, the method of the invention provides for the prediction of a measurement value using a Mixtures of Experts (MOE) algorithm.
The raw signal can be obtained using any suitable sensing methodology including, for example, methods which rely on direct contact of a sensing apparatus with the biological system; methods which extract samples from the biological system by invasive, minimally invasive, and non-invasive sampling techniques, wherein the sensing apparatus is contacted with the extracted sample; methods which rely on indirect contact of a sensing apparatus with the biological system; and the like. In preferred embodiments of the invention, methods are used to extract samples from the biological sample using minimally invasive or non-invasive sampling techniques. The sensing apparatus used with any of the above-noted methods can employ any suitable sensing element to provide the raw signal including, but not limited to, physical, chemical, electrochemical, photochemical, spectrophotometric, polarimetric, calorimetric, radiometric, or like elements. In preferred embodiments of the invention, a biosensor is used which comprises an electrochemical sensing element.
In one particular embodiment of the invention, the raw signal is obtained using a transdermal sampling system that is placed in operative contact with a skin or mucosal surface of the biological system. The sampling system transdermally extracts the analyte from the biological system using any appropriate sampling technique, for example, iontophoresis. The transdermal sampling system is maintained in operative contact with the skin or mucosal surface of the biological system to provide for continual or continuous analyte measurement.
In a preferred embodiment of the invention, a Mixtures of Experts algorithm is used to predict measurement values. The general Mixtures of Experts algorithm is represented by the following series of equations: where the individual experts have a linear form:                     An        =                              ∑                          i              =              1                        n                    ⁢                      xe2x80x83                    ⁢                                    An              i                        ⁢                          w              i                                                          (        1        )            
wherein (An) is an analyte of interest, n is the number of experts, Ani is the analyte predicted by Expert i; and wi is a parameter, and the individual experts Ani are further defined by the expression shown as Equation (2)                               An          i                =                                            ∑                              j                =                1                            m                        ⁢                                          a                ij                            ⁢                              p                j                                              +                      z            i                                              (        2        )            
wherein, Ani is the analyte predicted by Expert i; Pj is one of m parameters, m is typically less than 100; aij are coefficients; and zi is a constant; and further where the weighting value, wi, is defined by the formula shown as Equation (3).                               w          i                =                              ⅇ                          d              i                                            [                                          ∑                                  k                  =                  1                                n                            ⁢                              ⅇ                                  d                  k                                                      ]                                              (        3        )            
where e refers to the exponential function and the dk (note that the di in the numerator of Equation 3 is one of the dk) are a parameter set analogous to Equation 2 that is used to determine the weights wi. The dk are given by Equation 4.                               d          k                =                                            ∑                              j                =                1                            m                        ⁢                                          α                jk                            ⁢                              P                j                                              +                      ω            k                                              (        4        )            
where xcex1jk is a coefficient, Pj is one of m parameters, and where xcfx89k is a constant.
Another object of the invention to use the Mixtures of Experts algorithm of the invention to predict blood glucose values. In one aspect, the method of the invention is used in conjunction with an iontophoretic sampling device that provides continual or continuous blood glucose measurements. In one embodiment the Mixtures of Experts algorithm is essentially as follows: where the individual experts have a linear form
BG=w1BG1+w2BG2+w3BG3xe2x80x83xe2x80x83(5)
wherein (BG) is blood glucose, there are three experts (n=3) and BGi is the analyte predicted by Expert i; wi is a parameter, and the individual Experts BGi are further defined by the expression shown as Equations 6, 7, and 8
BG1=p1(time)+q1(active)+r1(signal)+s1(BG|cp)+t1xe2x80x83xe2x80x83(6)
BG2=p2(time)+q2(active)+r2(signal)+s2(BG|cp)+t2xe2x80x83xe2x80x83(7)
BG3=p3(time)+q3(active)+r3(signal)+s3(BG|cp)+t3xe2x80x83xe2x80x83(8)
wherein, BGi is the analyte predicted by Expert i; parameters include, time (elapsed time since the sampling system was placed in operative contact with said biological system), active (active signal), signal (calibrated signal), and BG/cp (blood glucose value at a calibration point); pi, qi, ri, and si are coefficients; and ti is a constant; and further where the weighting value, wi, is defined by the formulas shown as Equations 9, 10, and 11                               w          1                =                              ⅇ                          d              1                                                          ⅇ                              d                1                                      +                          ⅇ                              d                2                                      +                          ⅇ                              d                3                                                                        (        9        )                                          w          2                =                              ⅇ                          d              2                                                          ⅇ                              d                1                                      +                          ⅇ                              d                2                                      +                          ⅇ                              d                3                                                                        (        10        )                                          w          3                =                              ⅇ                          d              3                                                          ⅇ                              d                1                                      +                          ⅇ                              d                2                                      +                          ⅇ                              d                3                                                                        (        11        )            
where e refers to the exponential function and di is a parameter set (analogous to Equations 6, 7, and 8) that are used to determine the weights wi, given by Equations 9, 10, and 11, and
d1=xcfx841(time)+xcex21(active)+xcex31(signal)+xcex41(BG|cp)+xcex51xe2x80x83xe2x80x83(12)
d2=xcfx842(time)+xcex22(active)+xcex32(signal)+xcex42(BG|cp)+xcex52xe2x80x83xe2x80x83(13)
d3=xcfx843(time)+xcex23(active)+xcex33(signal)+xcex43(BG|cp)+xcex53xe2x80x83xe2x80x83(14)
where xcfx84i, xcex2i, xcex3i and xcex4i are coefficients, and where xcex5i is a constant.
In another embodiment for the prediction of blood glucose values, the Mixtures of Experts algorithm is essentially as follows: where the individual experts have a linear form
BG=w1BG1+w2BG2+w3BG3xe2x80x83xe2x80x83(15)
wherein (BG) is blood glucose, there are three experts (n=3) and BGi is the analyte predicted by Expert i; wi is a parameter, and the individual Experts BGi are further defined by the expression shown as Equations 16, 17, and 18
BG1=p1(timec)+q1(active)+r1(signal)+s1(BG|cp)+t1xe2x80x83xe2x80x83(16)
BG2=p2(timec)+q2(active)+r2(signal)+s2(BG|cp)+t2xe2x80x83xe2x80x83(17)
BG3=p3(timec)+q3(active)+r3(signal)+s3(BG|cp)+t3xe2x80x83xe2x80x83(18)
wherein, BGi is the analyte predicted by Expert i; parameters include, timec (elapsed time since calibration of said sampling system), active (active signal), signal (calibrated signal), and BG/cp (blood glucose value at a calibration point); pi, qi, ri, and si are coefficients; and ti is a constant; and further where the weighting value, wi, is defined by the formulas shown as Equations 19, 20, and 21                               w          1                =                              ⅇ                          d              1                                                          ⅇ                              d                1                                      +                          ⅇ                              d                2                                      +                          ⅇ                              d                3                                                                        (        19        )                                          w          2                =                              ⅇ                          d              2                                                          ⅇ                              d                1                                      +                          ⅇ                              d                2                                      +                          ⅇ                              d                3                                                                        (        20        )                                          w          3                =                              ⅇ                          d              3                                                          ⅇ                              d                1                                      +                          ⅇ                              d                2                                      +                          ⅇ                              d                3                                                                        (        21        )            
where e refers to the exponential function and di is a parameter set (analogous to Equations 6, 7, and 8) that are used to determine the weights wi, given by Equations 19, 20, and 21, and
d1=xcfx841(timec)+xcex21(active)+xcex31(signal)+xcex41(BG|cp)+xcex51xe2x80x83xe2x80x83(22)
d2=xcfx842(timec)+xcex22(active)+xcex32(signal)+xcex42(BG|cp)+xcex52xe2x80x83xe2x80x83(23)
d3=xcfx843(timec)+xcex23(active)+xcex33(signal)+xcex43(BG|cp)+xcex53xe2x80x83xe2x80x83(24)
where xcfx84i, xcex2i, xcex3i and xcex4i are coefficients, and where xcex5i is a constant.
Parameters can be substituted, and/or other parameters can be included in these calculations, for example, time parameters can be varied (e.g., as described above, elapsed time since the sampling system was placed in contact with a biological system, or elapsed time since the sampling system was calibrated) or multiple time parameters can be used in the same equation where these parameters are appropriately weighted. Further parameters include, but are not limited to, temperature, ionophoretic voltage, and skin conductivity. In addition, a calibration check can be used to insure an efficacious calibration.
A further object of the invention to provide a method for measuring an analyte, for example, blood glucose, in a subject. In one embodiment, the method entails operatively contacting a glucose sensing apparatus with the subject to detect blood glucose and thus obtain a raw signal from the sensing apparatus. The raw signal is specifically related to the glucose, and is converted into a measurement value indicative of the subject""s blood glucose concentration using a calibration step. In one aspect of the invention, the sensing apparatus is a near-IR spectrometer. In another aspect of the invention, the sensing means comprises a biosensor having an electrochemical sensing element.
It is also an object of the invention to provide a monitoring system for continually or continuously measuring an analyte present in a biological system. The monitoring system is formed from the operative combination of a sampling means, a sensing means, and a microprocessor means which controls the sampling means and the sensing means. The sampling means is used to continually or continuously extract the analyte from the biological system across a skin or mucosal surface of said biological system. The sensing means is arranged in operative contact with the analyte extracted by the sampling means, such that the sensing means can obtain a raw signal from the extracted analyte which signal is specifically related to the analyte. The microprocessor means communicates with the sampling means and the sensing means, and is used to: (a) control the sampling means and the sensing means to obtain a series of raw signals at selected time intervals during a continual or continuous measurement period; (b) correlate the raw signals with measurement values indicative of the concentration of analyte present in the biological system; and (c) predict a measurement value using the Mixtures of Experts algorithm. In one aspect, the monitoring system uses an iontophoretic current to extract the analyte from the biological system.
It is a further object of the invention to provide a monitoring system for measuring blood glucose in a subject. The monitoring system is formed from an operative combination of a sensing means and a microprocessor means. The sensing means is adapted for operative contact with the subject or with a glucose-containing sample extracted from the subject, and is used to obtain a raw signal specifically related to blood glucose in the subject. The microprocessor means communicates with the sensing means, and is used to: (a) control the sensing means to obtain a series of raw signals (specifically related to blood glucose) at selected time intervals; (b) correlate the raw signals with measurement values indicative of the concentration of blood glucose present in the subject; and (c) predict a measurement value using the Mixtures of Experts algorithm.
In a further aspect, the monitoring system comprises a biosensor having an electrochemical sensing element. In another aspect, the monitoring system comprises a near-IR spectrometer.
Additional objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following, or may be learned by practice of the invention.